An Introduction to Financial Option Valuation
Mathematics, Stochastics and Computation

This textbook provides an introduction to financial option valuation for undergraduates. Solutions available from solutions@cambridge.org.

Desmond J. Higham (Author)

9780521547574, Cambridge University Press

Paperback, published 15 April 2004

296 pages, 120 exercises
24.1 x 17 x 1.8 cm, 0.48 kg

'The material is presented in a … vivid and pedagogical manner. …It could equally well be ready by people with limited mathematical knowledge wanting to learn the basics of mathematical finance …' Zentralblatt MATH

This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.

1. Introduction
2. Option valuation preliminaries
3. Random variables
4. Computer simulation
5. Asset price movement
6. Asset price model: part I
7. Asset price model: part II
8. Black–Scholes PDE and formulas
9. More on hedging
10. The Greeks
11. More on the Black–Scholes formulas
12. Risk neutrality
13. Solving a nonlinear equation
14. Implied volatility
15. The Monte Carlo method
16. The binomial method
17. Cash-or-nothing options
18. American options
19. Exotic options
20. Historical volatility
21. Monte Carlo part II: variance reduction by antithetic variates
22. Monte Carlo part III: variance reduction by control variates
23. Finite difference methods
24. Finite difference methods for the Black–Scholes PDE.

Subject Areas: Applied mathematics [PBW], Finance [KFF]